{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neurodynamics Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Contents**:\n",
    "\n",
    "- [Phase Plane Analysis](#Phase-Plane-Analysis)\n",
    "- [Bifurcation Analysis](#Bifurcation-Analysis)\n",
    "- [Fast-Slow System Bifurcation](#Fast-Slow-System-Bifurcation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to the flexible and effecient *neurodynamics simulation*, another ambition of BrainPy is to provide an integrative platform for **neurodynamics analysis**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is known to us all, dynamics analysis is necessary in neurodynamics. This is because blind simulation of nonlinear systems is likely to produce few results or misleading results. For example, attractors and repellors can be easily obtained through simulation by time forward and backward, while saddles can be hard to find. \n",
    "\n",
    "Currently, BrainPy supports neurodynamics analysis for low-dimensional dynamical systems. Specifically, BrainPy provides the following methods for dynamics analysis:\n",
    "\n",
    "1. phase plane analysis for one-dimensional and two-dimensional systems;\n",
    "2. codimension one and codimension two bifurcation analysis;\n",
    "3. bifurcation analysis of the fast-slow system. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, I will illustrate how to do neuron dynamics analysis in BrainPy and how BrainPy implements it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-25T03:10:39.678453Z",
     "start_time": "2021-03-25T03:10:36.763061Z"
    }
   },
   "outputs": [],
   "source": [
    "import brainpy as bp\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phase Plane Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, I will illustrate how to do phase plane analysis by using a well-known neuron model FitzHugh-Nagumo model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**FitzHugh-Nagumo model**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The FitzHugh-Nagumo model is given by:\n",
    "\n",
    "$$ \n",
    "\\frac {dV} {dt} = V(1 - \\frac {V^2} 3) - w + I_{ext} \\\\\n",
    "\\tau \\frac {dw} {dt} = V + a - b w \n",
    "$$\n",
    "\n",
    "There are two variables $V$ and $w$, so this is a two-dimensional system with three parameters $a, b$ and $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:18.866966Z",
     "start_time": "2021-03-24T11:58:18.854001Z"
    }
   },
   "outputs": [],
   "source": [
    "a=0.7;  b=0.8;  tau=12.5;  Vth=1.9\n",
    "\n",
    "@bp.odeint\n",
    "def int_fhn(V, w, t, Iext):\n",
    "    dw = (V + a - b * w) / tau\n",
    "    dV = V - V * V * V / 3 - w + Iext\n",
    "    return dV, dw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Phase Plane Analysis is implemented in `brainpy.analysis.PhasePlane`. It receives the following parameters: \n",
    "\n",
    "- ``integrals``: The integral functions to be analysis. \n",
    "- ``target_vars``: The variables to be analuzed. It must a dictionary with the format of `{var: variable range}`.\n",
    "- ``fixed_vars``: The variables to be fixed (optional).\n",
    "- ``pars_update``: Parameters to update (optional)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`brainpy.analysis.PhasePlane` provides interface to analyze the system's \n",
    "\n",
    "- **nullcline**: The zero-growth isoclines, such as $g(x, y)=0$ and $g(x, y)=0$.\n",
    "- **fixed points**: The equilibrium points of the system, which are located at all of the nullclines intersect.\n",
    "- **vector filed**: The vector field of the system.\n",
    "- **Trajectory**: A given simulation trajectory with the fixed variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we perform a phase plane analysis with parameters $a=0.7, b=0.8, \\tau=12.5$, and input $I_{ext} = 0.8$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:24.172655Z",
     "start_time": "2021-03-24T11:58:18.870967Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot nullcline ...\n",
      "SymPy solve \"int_fhn(V, w) = 0\" to \"w = f(V, )\", success.\n",
      "SymPy solve \"int_fhn(V, w) = 0\" to \"w = f(V, )\", success.\n",
      "plot vector field ...\n",
      "plot fixed point ...\n",
      "SymPy solve derivative of \"int_fhn(V, w)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w)\" by \"w\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w)\" by \"w\", success.\n",
      "Fixed point #1 at V=-0.27290095899729705, w=0.5338738012533786 is a unstable node.\n",
      "plot trajectory ...\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "analyzer = bp.analysis.PhasePlane(\n",
    "    integrals=int_fhn,\n",
    "    target_vars={'V': [-3, 3], 'w': [-3., 3.]},\n",
    "    pars_update={'Iext': 0.8})\n",
    "analyzer.plot_nullcline()\n",
    "analyzer.plot_vector_field()\n",
    "analyzer.plot_fixed_point()\n",
    "analyzer.plot_trajectory([{'V': -2.8, 'w': -1.8}],\n",
    "                         duration=100.,\n",
    "                         show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see an unstable-node at the point (v=-0.27, w=0.53) inside a limit cycle. Then we can run a simulation with the same parameters and initial values to see the periodic activity that correspond to the limit cycle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:24.378721Z",
     "start_time": "2021-03-24T11:58:24.172655Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "class FHN(bp.NeuGroup):\n",
    "    target_backend = 'numpy'\n",
    "    \n",
    "    def __init__(self, num, **kwargs):\n",
    "        self.V = np.ones(num) * -2.8\n",
    "        self.w = np.ones(num) * -1.8\n",
    "        self.Iext = np.zeros(num) \n",
    "        super(FHN, self).__init__(size=num, **kwargs)\n",
    "    \n",
    "    def update(self, _t):\n",
    "        self.V, self.w = int_fhn(self.V, self.w, _t, self.Iext)\n",
    "\n",
    "        \n",
    "group = FHN(1, monitors=['V', 'w'])\n",
    "group.run(100., inputs=('Iext', 0.8, '=')) \n",
    "bp.visualize.line_plot(group.mon.ts, group.mon.V, legend='v', ) \n",
    "bp.visualize.line_plot(group.mon.ts, group.mon.w, legend='w', show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `fixed_vars` can be used to specify the neuron model's state `ST`, it can also be used to specify the functional arguments in integrators (like the `Iext` in `int_v()`). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bifurcation Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bifurcation analysis is implemented within `brainpy.analysis.Bifurcation`. Which support codimension-1 and codimension-2 bifurcation analysis. Specifically, it receives the following parameter settings: \n",
    "\n",
    "- ``integrals``: The integral functions to be analysis.\n",
    "- ``target_pars``: The target parameters. Must be a dictionary with the format of `{par: parameter range}`. \n",
    "- ``target_vars``: The target variables. Must be a dictionary with the format of `{var: variable range}`. \n",
    "- ``fixed_vars``: The fixed variables.\n",
    "- ``pars_update``: The parameters to update."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Codimension 1 bifurcation analysis**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will first see the codimension 1 bifurcation anlysis of the model. For example, we vary the input $I_{ext}$ between 0 to 1 and see how the system change it's stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:26.557712Z",
     "start_time": "2021-03-24T11:58:24.381727Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot bifurcation ...\n",
      "SymPy solve \"int_fhn(V, w, Iext) = 0\" to \"w = f(V, Iext)\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, Iext)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, Iext)\" by \"w\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, Iext)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, Iext)\" by \"w\", success.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "analyzer = bp.analysis.Bifurcation(\n",
    "    integrals=int_fhn,\n",
    "    target_pars={'Iext': [0., 1.]},\n",
    "    target_vars={'V': [-3, 3], 'w': [-3., 3.]},\n",
    "    numerical_resolution=0.001,\n",
    ")\n",
    "analyzer.plot_bifurcation(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Codimension 2 bifurcation analysis**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We simulaneously change $I_{ext}$ and parameter $a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:29.634679Z",
     "start_time": "2021-03-24T11:58:26.561712Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot bifurcation ...\n",
      "SymPy solve \"int_fhn(V, w, a, Iext) = 0\" to \"w = f(V, a,Iext)\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, a, Iext)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, a, Iext)\" by \"w\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, a, Iext)\" by \"V\", success.\n",
      "SymPy solve derivative of \"int_fhn(V, w, a, Iext)\" by \"w\", success.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from collections import OrderedDict\n",
    "\n",
    "analyzer = bp.analysis.Bifurcation(\n",
    "    integrals=int_fhn,\n",
    "    target_pars=OrderedDict(a=[0.5, 1.], Iext=[0., 1.]),\n",
    "    target_vars=OrderedDict(V=[-3, 3], w=[-3., 3.]),\n",
    "    numerical_resolution=0.01,\n",
    ")\n",
    "analyzer.plot_bifurcation(show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fast-Slow System Bifurcation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BrainPy also provides a tool for fast-slow system bifurcation analysis by using `brainpy.analysis.FastSlowBifurcation`. This method is proposed by John Rinzel [1, 2, 3]. (J Rinzel, 1985, 1986, 1987) proposed that in a fast-slow dynamical system, we can treat the slow variables as the bifurcation parameters, and then study how the different value of slow variables affect the bifurcation of the fast sub-system.\n",
    "\n",
    "\n",
    "`brainpy.analysis.FastSlowBifurcation` is very usefull in the bursting neuron analysis. I will illustrate this by using the Hindmarsh-Rose model. The Hindmarsh–Rose model of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron. Its dynamics are governed by:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{d V}{d t} &= y - a V^3 + b V^2 - z + I\\\\\n",
    "\\frac{d y}{d t} &= c - d V^2 - y\\\\\n",
    "\\frac{d z}{d t} &= r (s (V - V_{rest}) - z)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, let's define the Hindmarsh–Rose model with BrainPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:29.650571Z",
     "start_time": "2021-03-24T11:58:29.637572Z"
    }
   },
   "outputs": [],
   "source": [
    "a = 1.; b = 3.; c = 1.; d = 5.; s = 4. \n",
    "x_r = -1.6; r = 0.001; Vth = 1.9\n",
    "\n",
    "@bp.odeint(method='rk4', dt=0.02)\n",
    "def int_hr(x, y, z, t, Isyn):\n",
    "    dx = y - a * x ** 3 + b * x * x - z + Isyn\n",
    "    dy = c - d * x * x - y\n",
    "    dz = r * (s * (x - x_r) - z)\n",
    "    return dx, dy, dz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now can start to analysis the underlying bifurcation mechanism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-24T11:58:37.282699Z",
     "start_time": "2021-03-24T11:58:29.658573Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot bifurcation ...\n",
      "SymPy solve \"int_hr(x, y, z) = 0\" to \"y = f(x, z)\", success.\n",
      "SymPy solve derivative of \"int_hr(x, y, z)\" by \"x\", success.\n",
      "SymPy solve derivative of \"int_hr(x, y, z)\" by \"y\", success.\n",
      "SymPy solve derivative of \"int_hr(x, y, z)\" by \"x\", success.\n",
      "SymPy solve derivative of \"int_hr(x, y, z)\" by \"y\", success.\n",
      "plot trajectory ...\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "analyzer = bp.analysis.FastSlowBifurcation(\n",
    "    integrals=int_hr,\n",
    "    fast_vars={'x': [-3, 3], 'y': [-10., 5.]},\n",
    "    slow_vars={'z': [-5., 5.]},\n",
    "    pars_update={'Isyn': 0.5},\n",
    "    numerical_resolution=0.001\n",
    ")\n",
    "analyzer.plot_bifurcation()\n",
    "analyzer.plot_trajectory([{'x': 1., 'y': 0., 'z': -0.0}],\n",
    "                         duration=100.,\n",
    "                         show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References**:\n",
    "\n",
    "[1] Rinzel, John. \"Bursting oscillations in an excitable membrane model.\" In Ordinary and partial differential  equations, pp. 304-316. Springer, Berlin, Heidelberg, 1985.\n",
    "           \n",
    "[2] Rinzel, John , and Y. S. Lee . On Different Mechanisms for Membrane Potential Bursting. Nonlinear Oscillations in Biology and Chemistry. Springer Berlin Heidelberg, 1986.\n",
    "\n",
    "[3] Rinzel, John. \"A formal classification of bursting mechanisms in excitable systems.\" In Mathematical topics in population biology, morphogenesis and neurosciences, pp. 267-281. Springer, Berlin, Heidelberg, 1987.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Outlook**\n",
    "\n",
    "In future, we will provide more analysis methods for various dynamical systems. We now also start to consider how to analyze the network model. Of course, we welcome your contributions on neurodynamics analysis. "
   ]
  }
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